Thijs J. H. Vlugt

Computing the Heat of Adsorption using Molecular Simulations: The Effect of Strong Coulombic Interactions

Molecular simulations are an important tool for the study of adsorption of hydrocarbons in nanoporous materials such as zeolites. The heat of adsorption is an important thermodynamic quantity that can be measured both in experiments and molecular simulations, and therefore it is often used to investigate the quality of a force field for a certain guest-host (g - h) system. In molecular simulations, the heat of adsorption in zeolites is often computed using either of the following methods: (1) using the Clausius-Clapeyron equation, which requires the partial derivative of the pressure with respect to temperature at constant loading, (2) using the energy difference between the host with and without a single guest molecule present, and (3) from energy/particle fluctuations in the grand-canonical ensemble. To calculate the heat of adsorption from experiments (besides direct calorimetry), only the first method is usually applicable. Although the computation of the heat of adsorption is straightforward for all-silica zeolites, severe difficulties arise when applying the conventional methods to systems with nonframework cations present. The reason for this is that these nonframework cations have very strong Coulombic interactions with the zeolite. We will present an alternative method based on biased interactions of guest molecules that suffers less from these difficulties. This method requires only a single simulation of the host structure. In addition, we will review some of the other important issues concerning the handling of these strong Coulombic interactions in simulating the adsorption of guest molecules. It turns out that the recently proposed Wolf method ( J. Chem. Phys. 1999, 110 , 8254 ) performs poorly for zeolites as a large cutoff radius is needed for convergence.

Molecular simulations of interacting nanocrystals.

We compute the potential of mean force for two gold nanocrystals capped by alkylthiols from atomistic simulations and show how variables such as temperature, capping molecule length, and the presence of solvent affect these interactions. Our main findings are (1) the equilibrium distance in vacuum always equals approximately 1.25 times the core diameter, (2) incomplete capping layers promote sintering, and (3) the presence of a good solvent results in purely repulsive interactions.

Molecular simulation of loading dependent diffusion in nanoporous materials using extended dynamically corrected transition state theory

A dynamically corrected transition state theory method is presented that is capable of computing quantitatively the self-diffusivity of adsorbed molecules in confined systems at nonzero loading. This extension to traditional transition state theory is free of additional assumptions and yields a diffusivity identical to that obtained by conventional molecular-dynamics simulations. While molecular-dynamics calculations are limited to relatively fast diffusing molecules, our approach extends the range of accessible time scales significantly beyond currently available methods. We show results for methane, ethane, and propane in LTL- and LTA-type zeolites over a wide range of temperatures and loadings, and demonstrate the extensibility of the method to mixtures.

Influence of isotherm inflection on diffusion in silicalite

Adsorption isotherms of benzene, p-xylene, n-hexane, n-heptane and branched alkanes in silicalite show inflection behaviour; this behaviour is adequately modelled using a dual-site Langmuir model. In this model we make a distinction between two sites with di⁄erent sorption characteristics: (1) site A which refer to the intersections between the straight channels and the zig-zag channels, and site B which refers to the channel interiors (straight or zig-zag channels). Using the Maxwell—Stefan theory of di⁄usion in zeolites, the influence of the isotherm inflection on the Fick di⁄usivity of pure components in silicalite is shown to be characterized by two extrema. For a mixture of n-hexane and 3-methyl pentane, the dual-site Langmuir model for the mixture predicts a curious maximum in the loading of the branched alkane; this mixture behaviour is confirmed by Configurational-Bias Monte Carlo simulations. The Maxwell—Stefan theory is used to demonstrate the possibility of separating the hydrocarbon isomers by permeation across a silicalite membrane. ( 1999 Elsevier Science Ltd. All rights reserved.

Time-dependent photoluminescence spectroscopy as a tool to measure the ligand exchange kinetics on a quantum dot surface

The exchange kinetics of native ligands that passivate CdSe quantum dots (hexadecylamine (HDA), trioctylphosphine oxide (TOPO), and trioctylphosphine (TOP)) by thiols is followed in situ. This is realized by measuring, in real-time, the decrease in emission intensity of the QDs upon addition of hexanethiol (HT) which quenches the emission. The effect of adding an excess of native ligands prior to thiol addition on the capping exchange is studied to provide insight in the bond strength and exchange kinetics of the individual surfactants. Temperature-dependent measurements reveal faster kinetics with increasing temperature. A kinetic model to describe the time-dependent measurements is introduced, taking into account the equilibrium between native ligands before thiol addition and describing the evolution of surface coverage by all ligands over time. The model allows us to extract the quenching rate for a single thiol ligand (0.004 ns(-1)) as well as exchange rates, equilibrium constants, activation energies, and changes in Gibbs free energy for replacement of the different native surfactants by HT. The analysis reveals that the substitution half-time of HDA by HT (72 s) is much shorter than for TOP (5 h) or TOPO (2.5 h) under the same conditions. The temperature dependence of the kinetics shows that the activation energy for exchange of HDA/TOPO by hexanethiol (1.6 kJ/mol) is much smaller than for TOP (20.9 kJ/mol).

Calculating thermodynamic properties from fluctuations at small scales.

We show how density and energy fluctuations of small nonperiodic systems embedded in a reservoir can be used to determine macroscopic thermodynamic properties like the enthalpy density and the thermodynamic correction factor. For mixtures, the same formalism leads to a very convenient method to obtain so-called total correlation function integrals, also often referred to as Kirkwood-Buff integrals. Using finite size scaling, the properties obtained for small systems can be extrapolated to the macroscopic system limit provided that the system is sufficiently far from the critical point. As derived in our previous work (Chem. Phys. Lett. 2011, 504, 199-201), the finite size scaling is significant and depends on 1/L, where L is the length of the small system in one dimension. By considering a reservoir with an ensemble of embedded small systems, we can use the scaling arising from surface effects to determine properties for macroscopic systems by extrapolation. We demonstrate this method for the WCA and LJ fluids, as well a for a heterogeneous system, i.e., argon adsorbed in silicalite-1 zeolite.

Kirkwood−Buff Integrals for Finite Volumes

Exact expressions for finite-volume Kirkwood-Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

Shape selectivity through entropy

Based on a comparison between measured and simulated adsorption properties, we demonstrate that a decrease in the Gibbs free energy of formation and adsorption—due to higher adsorption entropy—satisfactorily explains the selective production and adsorption of the most compact, branched paraffins in n-hexadecane hydroconversion in molecular sieves with pore diameters of ∼ 0.75 nm. Adsorption entropy is important because the pores are saturated with reactant, and because the adsorbed phase is not at gas-phase chemical equilibrium. This explanation supplants the traditional kinetic explanation involving changes in the Gibbs free energy of formation of the relevant transition states. Instead, we attribute the effect of molecular sieve structure on the branched paraffin yield to a redirection of the hydroisomerization reactions away from the gas-phase chemical equilibrium distribution, commensurate with the Gibbs free energy of adsorption of the isomers inside the pores. These shape-selective changes to the reaction rates appear to be as ubiquitous as those originating from steric constraints imposed on intracrystalline diffusion and reaction rates. This would make adsorption-induced changes in the Gibbs free energy of formation of reactants, intermediates, and products a missing cornerstone in traditional shape selectivity theory.  2003 Elsevier Science (USA). All rights reserved.

On the Mechanism Behind the Instability of Isoreticular Metal-Organic Frameworks (IRMOFs) in Humid Environments

Increasing the resistance to humid environments is mandatory for the implementation of isoreticular metal-organic frameworks (IRMOFs) in industry. To date, the causes behind the sensitivity of [Zn(4)(μ(4)-O)(μ-bdc)(3)](8)(IRMOF-1; bdc=1,4-benzenedicarboxylate) to water remain still open. A multiscale scheme that combines Monte Carlo simulations, density functional theory and first-principles Born-Oppenheimer molecular dynamics on IRMOF-1 was employed to unravel the underlying atomistic mechanism responsible for lattice disruption. At very low water contents, H(2)O molecules are isolated in the lattice but provoke a dynamic opening of the terephthalic acid, and the lattice collapse occurs at about 6% water weight at room temperature. The ability of Zn to form fivefold coordination spheres and the increasing basicity of water when forming clusters are responsible for the displacement of the organic linker. The present results pave the way for synthetic challenges with new target linkers that might provide more robust IRMOF structures.

Understanding interactions between capped nanocrystals: three-body and chain packing effects.

Self-assembly of capped nanocrystals (NC) attracted a lot of attention over the past decade. Despite progress in manufacturing of NC superstructures, the current understanding of their mechanical and thermodynamic stability is still limited. For further applications, it is crucial to find the origin and the magnitude of the interactions that keep self-assembled NCs together, and it is desirable to find a way to rationally manipulate these interactions. We report on molecular simulations of interacting gold NCs protected by capping molecules. We computed the potential of mean force for pairs and triplets of NCs of different size (1.8-3.7 nm) with varying ligand length (ethanethiol-dodecanethiol) in vacuum. Pair interactions are strongly attractive due to attractive van der Waals interactions between ligand molecules. Three-body interaction results in an energy penalty when the capping layers overlap pairwise. This effect contributes up to 20% to the total energy for short ligands. For longer ligands, the three-body effects are so large that formation of NC chains becomes energetically more favorable than close packing of capped NCs at low concentrations, in line with experimental observations. To explain the equilibrium distance for two or more NCs, the overlap cone model is introduced. This model is based on relatively simple ligand packing arguments. In particular, it can correctly explain why the equilibrium distance for a pair of capped NCs is always approximately 1.25 times the core diameter independently on the ligand length, as found in our previous work [Schapotschnikow, R. Pool, and T. J. H. Vlugt, Nano Lett. 8, 2930 (2008)]. We make predictions for which ligands capped NCs self-assemble into highly stable three-dimensional structures, and for which they form high-quality monolayers.